The story takes place in Georgia. We don't have much in the way of a description of the original setting. This tale begins in a nameless city where the family lives, and takes us various places along the road as the family travels. Plenty of local color – there are the old plantations that get passed, and Red Sammy's roadside barbeque joint.
The second half of the story takes place in the ditch in the middle of nowhere where the family lands after running off the road. We're told the ditch is about ten feet below the road, and lies between the road and a "tall and dark and deep" forest. There's forest on the other side of the road too, so the forest "looms" menacingly over the scene on both sides. This part of the story is like a staged play: the site of the action doesn't move, the ditch is the stage, and the forest is "backstage," where characters are taken. We only learn what's going happening from the noises people make (usually screams or gunshots).
As for the time, the era of the story is never explicitly defined, but given the cars and the mention of Gone With the Wind (published as a book in 1936 and released as a movie in 1939), we can guess it's the 1940's or later. Since there's no mention of a war going on, and the grandmother says that "the way Europe acted you would think we were made of money" (44), it's almost certainly after the war, meaning late '40s or early '50s. That would be right about when O'Connor wrote the story (1953) anyway.
The particular timing of the story is a more interesting issue. We know that the family leaves their home in the morning, and that they leave Red Sammy's in the "hot afternoon" (presumably it's summer). We don't actually know how late it is, though, when they land in the ditch. The narrator never says it's night, and the grandmother says it's a beautiful day. We also know there's no sun in the sky. Does that mean it's around sunset?